Best of Three Normals
X₁, X₂, X₃ are independent standard normal random variables. What is E[max(X₁, X₂, X₃)]? Give an exact closed form, or a decimal rounded to 4 places.
Related problems & prerequisites
Worth solving first
- The Ratio of Two Normals 7.0/10
- Inside the Unit Circle 7.0/10
- Correlation of the Extremes 5.0/10
Source: Classic Gaussian exercise in wide circulation; no traceable original source. Statement written for AxiomIQ.